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Published on: June 2, 2010
Uniqueness of the gaussian kernel for scale-space filtering
J Babaud1, A P Witkin, M Baudin
1Schlumberger Computer Aided Systems, Palo Alto, CA 94304.
Abstract:
Scale-space filtering constructs hierarchic symbolic signal descriptions by transforming the signal into a continuum of versions of the original signal convolved with a kernal containing a scale or bandwidth parameter. It is shown that the Gaussian probability density function is the only kernel in a broad class for which first-order maxima and minima, respectively, increase and decrease when the bandwidth of the filter is increased. The consequences of this result are explored when the signal¿or its image by a linear differential operator¿is analyzed in terms of zero-crossing contours of the transform in scale-space.
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